Armature is moving weird on Unity made in Blender
To rule out Unity from the equation there are 2 things to try.
1. try removing the key frame optimisation in the inspector / animation settings.
2. Import your exported FBX back into a new blender scene, do you see the same issue in blander.

If 1 fixes it, it’s the Unity keyframe optimisation settings.

If 2 shows the same issue as you get in Unity then the issue lies in the rig and or blender export.